When an item is archived or deleted, existing automatic reminders linked to the item will still be sent, but no new reminders will be created based on the item after it has been archived or deleted. When you archive or delete an item that is connected to an automatic reminder rule, you will see a warning before confirming the action.
When you delete or archive an item that is connected to a reminder creation rule, remember to update your automatic reminder rule with a new item or other conditions to make sure that the reminder continues to function as intended.